The image reconstruction can also be implemented by calculating the correlations between the measured intensity data \(I_{t}\)  and the time series \(a_{ijt}\)  in the original patterns \(C_{ij}=\sum ^{M-1}_{t=0}I_t a_{ijt}\)  [1]}, [2]}, [3]}. Filling an \(H \times W\)  matrix with all the \(C_{ij}\)  at their locations \(\left(i,j\right)\)  will yield an image of the object. However, the visibility of the image reconstructed by correlation is lower than that of the image produced by FFT-based methods,
because in this case the correlation is done without a shift in time, leading to a non-trivial contribution of the white noise. Fig. REF (d) compares the visibility of the images generated by the three algorithms for different \(\beta \) . It is worth mentioning that the performances of STEP-FT and STEP-CS are almost independent of \(\beta \) : they have similar visibility over the investigated range of \(\beta \)  and show saturation behaviors. This means high-quality images may be obtained with small data sets, and thus consume less time on measurement and computation. On the other hand, the correlation has the worst overall performance and is sensitive to the value of \(\beta \) . Therefore, high-quality images may only be acquired with a large number of data points.
